Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

Busłowicz, Mikołaj; Ruszewski, Andrzej

doi:10.2478/v10006-012-0030-9

Abstract

Asymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

References

Bistritz, Y. (2003). A stability test for continuous-discrete bivariate polynomials, Proceedings of the 2003 IEEE International Symposium on Circuits and Systems, Bangkok, Thailand, Vol. 3, pp. 682-685.
Search in Google Scholar
Bistritz, Y. (2004). Immittance and telepolation-based procedures to test stability of continuous-discrete bivariate polynomials, Proceedings of the 2004 IEEE International Symposium on Circuits and Systems, Vancouver, Canada, Vol. 3, pp. 293-296.
Search in Google Scholar
Busłowicz, M. (1997). Stability of Linear Time-invariant Systems with Uncertain Parameters, Technical University of Białystok, Białystok, (in Polish).
Search in Google Scholar
Busłowicz, M. (2010a). Robust stability of the new general 2D model of a class of continuous-discrete linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(4): 561-565.10.2478/v10175-010-0056-9
Search in Google Scholar
Busłowicz, M. (2010b). Stability and robust stability conditions for general model of scalar continuous-discrete linear systems, Pomiary, Automatyka, Kontrola 56(2): 133-135.10.2478/v10175-010-0056-9
Search in Google Scholar
Busłowicz, M. (2011a). Computational methods for investigation of stability of models of 2D continuous-discrete linear systems, Journal of Automation, Mobile Robotics and Intelligent Systems 5(1): 3-7.
Search in Google Scholar
Busłowicz, M. (2011b). Improved stability and robust stability conditions for general model of scalar continuous-discrete linear systems, Pomiary, Automatyka, Kontrola 57(2): 188-189.10.2478/v10175-010-0056-9
Search in Google Scholar
Busłowicz, M. and Ruszewski, A. (2011). Stability investigation of continuous-discrete linear systems, Pomiary, Automatyka, Robotyka 2(2): 566-575, (on CD-ROM, in Polish).
Search in Google Scholar
Dymkov, M. (2005). Extremal Problems in Multiparameter Control Systems, BGEU Press, Minsk, (in Russian).
Search in Google Scholar
Dymkov, M., Gaishun, I., Rogers, E., Gałkowski, K. and Owens, D. H. (2004). Control theory for a class of 2D continuousdiscrete linear systems, International Journal of Control 77(9): 847-860.10.1080/00207170410001726796
Search in Google Scholar
Dymkov M., Rogers E., Dymkou S., Gałkowski, K. and Owens D. H. (2003). Delay system approach to linear differential repetitive processes, Proceedings of the IFAC Workshop on Time-Delay Systems (TDS 2003), Rocquencourt, France, (CD-ROM).10.1016/S1474-6670(17)33348-7
Search in Google Scholar
Gałkowski, K., Rogers, E., Paszke, W. and Owens, D. H. (2003). Linear repetitive process control theory applied to a physical example, International Journal of Applied Mathematics and Computer Science 13(1): 87-99.
Search in Google Scholar
Guiver, J. P. and Bose, N. K. (1981). On test for zero-sets of multivariate polynomials in noncompact polynomials, Proceedings of the IEEE 69(4): 467-469.10.1109/PROC.1981.11992
Search in Google Scholar
Hespanha, J. (2004). Stochastic hybrid systems: Application to communication networks, Technical report, Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA.10.1007/978-3-540-24743-2_26
Search in Google Scholar
Johanson, K., Lygeros, J. and Sastry, S. (2004). Modelling hybrid systems, in H. Unbehauen (Ed.), Encyclopedia of Life Support Systems, EOLSS, Berlin.
Search in Google Scholar
Kaczorek, T. (1998). Vectors and Matrices in Automatics and Electrotechnics, WNT, Warsaw, p. 70, (in Polish).
Search in Google Scholar
Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.10.1007/978-1-4471-0221-2
Search in Google Scholar
Kaczorek, T. (2007). Positive 2D hybrid linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 55(4): 351-358.
Search in Google Scholar
Kaczorek, T. (2008a). Positive fractional 2D hybrid linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(3): 273-277.
Search in Google Scholar
Kaczorek, T. (2008b). Realization problem for positive 2D hybrid systems, International Journal for Computation and Mathematics in Electrical and Electronic Engineering, COMPEL 27(3): 613-623.10.1108/03321640810861061
Search in Google Scholar
Kaczorek, T. (2011). Selected Problems of Fractional Systems Theory, Lecture Notes in Control and Information Sciences, Vol. 411, Springer-Verlag, Berlin.
Search in Google Scholar
Kaczorek, T., Marchenko, V. and Sajewski, Ł. (2008). Solvability of 2D hybrid linear systems—Comparison of the different methods, Acta Mechanica et Automatica 2(2): 59-66.
Search in Google Scholar
Keel, L. H. and Bhattacharyya, S. P. (2000). A generalization of Mikhailov's criterion with applications, Proceedings of the American Control Conference, Chicago, IL, USA, Vol. 6, pp. 4311-4315.
Search in Google Scholar
Liberzon, D. (2003). Switching in Systems and Control, Birkhauser, Boston, MA.10.1007/978-1-4612-0017-8
Search in Google Scholar
Sajewski, Ł. (2009). Solution of 2D singular hybrid linear systems, Kybernetes 38(7/8): 1079-1092.10.1108/03684920910976835
Search in Google Scholar
Marchenko V. M. and Loiseau J. J. (2009). On the stability of hybrid difference-differential systems, Differential Equation 45(5), 743-756.10.1134/S0012266109050139
Search in Google Scholar
Rogers, E., Gałkowski, K. and Owens, D. H. (2007). Control Systems Theory and Applications for Linear Repetitive Processes, Lecture Notes in Control and Information Sciences, Vol. 349, Springer-Verlag, Berlin.
Search in Google Scholar
Xiao, Y. (2001). Stability test for 2-D continuous-discrete systems. Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, USA, Vol. 4, pp. 3649-3654.10.1109/CDC.2001.980427
Search in Google Scholar

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

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